Radiation collimators are used in a multitude of applications, including focused or directional radiation emission or radiation imagery and sensing. Radiation imagery applications include gamma and X-ray cameras and devices utilizing radiation camera settings. Radiation emission applications include radiation therapy devices, such as the gamma knife (U.S. Pat. No. 6,968,036), or the Linac (U.S. Pat. No. 6,459,769B1). Other applications, such as industrial material quality testing and crack detection (U.S. Pat. No. 4,680,470) utilize radiation imagery as well as radiation emission, both requiring the use of collimators. The art uses collimators in a variety of spatial or structural arrangements or distributions, such as hemispheres (U.S. Pat. No. 6,968,036 B2; U.S. Pat. No. 5,448,611), linear distributions, or “fan-beam” collimators (GB 1,126,767; JP20002318283). Widely used are cylindrical collimators and pinhole collimators (U.S. Pat. No. 4,348,591; U.S. Pat. No. 6,114,702), in a variety of spatial distributions (U.S. Pat. No. 5,270,549). Recent applications disclose laminar/superposed adjustable collimators (U.S. Pat. No. 5,436,958), single-leaf elliptical collimators (WO 2006/015077A1), or multi-leaf adjustable collimators (U.S. Pat. No. 6,388,816 B2; U.S. Pat. No. 6,714,627; U.S. Pat. No. 7,095,823 B2). However, none of these art collimator designs takes into account the radiation attenuation law (i.e., the attenuation is proportional to the inverse exponential of the shielding thickness through which the radiation passes) in assessing the directivity characteristic (radiation diagram) of the collimators. These limits affect the directional precision in the case of radiation emitters and the resolution in the case of imagery applications (Teodorescu).
Conchoids have frequently been used in patents, but never in the art of radiation collimators. Patents include using conchoids for clock mechanisms (U.S. Pat. No. 6,809,992), for metal cutting tools (U.S. Pat. No. 2,053,392), for antenna steering devices (U.S. Pat. No. 6,766,166), for tape recorders (U.S. Pat. No. 3,443,447), as well as for optical lenses (U.S. Pat. No. 880,208). Other publications illustrate the use of the Nicomedes conchoid in optimization problems, such as in (Kacimov).